Finite Group Databasebeta

← #30620270

Subgroups — #30620270

Order 15616.

1202 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840794C211yesmaximal, characteristic, complemented
2C2×#16840789C211yesmaximal, characteristic, complemented
3#21461993C211yesmaximal, characteristic, complemented
4#21461988C211yesmaximal, characteristic, complemented
5#21461796C211yesmaximal, characteristic, complemented
6#21461793C211yesmaximal, characteristic, complemented
7#21461793C211yesmaximal, characteristic, complemented
8#21461792C211yesmaximal, characteristic, complemented
9#21461712C211yesmaximal, characteristic, complemented
10#21461711C211yesmaximal, characteristic, complemented
11#21461677C211yesmaximal, characteristic, complemented
12#21461549C211yesmaximal, characteristic, complemented
13#21461485C211yesmaximal, characteristic, complemented
14#21461480C211yesmaximal, characteristic, complemented
15C2×#16840291C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840794—24no—
21#16840789—24no—
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×C22⋊#92420C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×#14519832C2211yescharacteristic
33C2×C4×#92420C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840291—24no—
47#16840291—24no—
48C2×#14519770C411yescharacteristic
49C2×#14519770C411yescharacteristic
50C2×#14519769C411yescharacteristic
51C2×#14519759C411yescharacteristic
52C2×#14519759C411yescharacteristic
53C2×#14519753C411yescharacteristic
54C2×#14519748C411yescharacteristic
55C2×Q8×Dic61C2211yescharacteristic
56C2×D4×Dic61C2211yescharacteristic
57C2×#14519737C2211yescharacteristic
58C2×#14519737C2211yescharacteristic
59C2×#14519733C2211yescharacteristic
60C2×#14519733C2211yescharacteristic
61C2×C42×D61C2211yescharacteristic
62C2×#124×C61C411yescharacteristic
63C2×#11758217—22no—
64C2×#11758217—22no—
65C2×#11758217—41no—
66C2×D61⋊C8—22no—
67C2×D61⋊C8—22no—
68C2×D61⋊C8—22no—
69C2×D61⋊C8—22no—
70C2×D61⋊C8—41no—
71C2×D61⋊C8—41no—
72C22×#92420—22no—
73C22×#92420—22no—
74C22×#92420—41no—
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83#14519844—22no—
84C4⋊#92420—22no—
85#14519834—22no—
86#14519834—22no—
87C22⋊#92420—22no—
88C22⋊#92420—22no—
89C22⋊#92420—22no—
90C22⋊#92420—22no—
91C22⋊#92420—41no—
92C22⋊#92420—41no—
93#14519832—22no—
94C4×#92420—22no—
95C22×C22⋊D61C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C23×Dic61C2311yescharacteristic
98C23×Dic61C2311yescharacteristic
99C22×C4×D61C2×C411yescharacteristic
100C22×C4×D61C2×C411yescharacteristic
101C22×C4×D61C2311yescharacteristic
102#14519770—24no—
103#14519770—24no—
104#14519769—24no—
105#14519759—24no—
106#14519759—24no—
107#14519753—24no—
108#14519748—24no—
109Q8×Dic61—22no—
110Q8×Dic61—22no—
111D4×Dic61—22no—
112D4×Dic61—22no—
113#14519737—22no—
114#14519737—22no—
115#14519737D414yes—
116#14519737D414yes—
117#14519733—22no—
118#14519733—22no—
119#14519733—22no—
120#14519733—22no—
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×C4⋊Dic61C2×C411yescharacteristic
123C2×C4⋊Dic61C2×C411yescharacteristic
124C2×C4⋊Dic61C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C2×#11758196C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×C22⋊Dic61C2×C411yescharacteristic
133C2×C22⋊Dic61C2×C411yescharacteristic
134C2×C22⋊Dic61C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2311yescharacteristic
139C2×C4×Dic61C2311yescharacteristic
140C2×C4×Dic61C2311yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142C42×D61—22no—
143C42×D61—22no—
144C22×Q8×C61C2×C411yescharacteristic
145C22×D4×C61C2×C411yescharacteristic
146#124×C61—24no—
147C2×C22⋊C4×C61C2×C411yescharacteristic
148C2×C22⋊C4×C61C2×C411yescharacteristic
149C2×C22⋊C4×C61C2×C411yescharacteristic
150C2×C22⋊C4×C61C2×C411yescharacteristic
151C2×C42×C61C2×C411yescharacteristic
152C24×C61C22×C411yescharacteristic
153C24×C61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×Q8×C61—22no—
156C2×Q8×C61—22no—
157C2×Q8×C61—41no—
158C2×D4×C61—22no—
159C2×D4×C61—22no—
160C2×D4×C61—41no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61C22⋊C414yes—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C2×D412yes—
189C22×Dic61C2×D412yes—
190C22×Dic61C2411yescharacteristic
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—41no—
201C2×C4×D61C2×D412yes—
202C2×C4×D61C2×D412yes—
203#11758217—44no—
204C2×#92420—21no—
205C2×#92420—21no—
206C2×#92420—21no—
207C2×#92420—21no—
208C2×#92420—21no—
209C2×#92420—21no—
210C2×#92420—21no—
211C2×#92420—21no—
212C2×#92420—21no—
213C2×#92420—21no—
214C2×#92420—21no—
215C2×#92420—21no—
216C2×#92420—21no—
217C2×#92420—21no—
218C2×#92420—21no—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420—21no—
223C2×#92420—21no—
224C2×#92420—21no—
225C2×#92420—21no—
226C2×#92420—44no—
227C2×#92420#4112yes—
228C2×#92420#4112yes—
229D61⋊C8—44no—
230D61⋊C8—44no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61C22⋊C414yes—
235C42×C61—22no—
236C22⋊Dic61—22no—
237C22⋊Dic61—22no—
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240#11758198—22no—
241#11758198C22⋊C414yes—
242C4⋊Dic61—22no—
243C4⋊Dic61—22no—
244C4⋊Dic61—22no—
245C4⋊Dic61—22no—
246#11758196—22no—
247#11758196—22no—
248#11758196—22no—
249#11758196—22no—
250#11758196—22no—
251#11758196C22⋊C414yes—
252C4×Dic61—22no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C4×Dic61—21no—
256C4×Dic61—21no—
257C4×Dic61—21no—
258C4×Dic61—21no—
259C4×Dic61C2×D412yes—
260C4×Dic61C2×D412yes—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61C2×C22⋊C412yes—
275C23×C61C23×C411yescharacteristic
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61C2×C22⋊C412yes—
281C22×D61#13112yes—
282C22×D61#13112yes—
283Q8×C61—44no—
284D4×C61—44no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61C2×C22⋊C412yes—
298C2×C4×C61C2×C22⋊C412yes—
299C2×C4×C61#13112yes—
300C22⋊D61—28no—
301C22⋊D61—44no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61C2×C22⋊C412yes—
327C2×Dic61C2×C22⋊C412yes—
328C2×Dic61C22×D411yescharacteristic
329C2×Dic61C22×D411yescharacteristic
330C2×Dic61C2×#4111yescharacteristic
331C2×Dic61C2×#4111yescharacteristic
332C2×Dic61H(5,𝔽2)11yescharacteristic
333C2×Dic612−1+411yescharacteristic
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—44no—
339C4×D61—44no—
340#92420—22no—
341#92420—22no—
342#92420—41no—
343#92420—41no—
344#92420—41no—
345#92420—41no—
346#92420—41no—
347#92420—41no—
348#22470—611nomaximal, Sylow
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61C22×C22⋊C411yescharacteristic
364C22×C61C4×#4111yescharacteristic
365C22×C61#52011yescharacteristic
366C22×C61C2×#13111yescharacteristic
367C22×C61C2×#13111yescharacteristic
368C22×C61C2×#13111yescharacteristic
369C22×C61#56811yescharacteristic
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—22no—
376C2×D61#40814yes—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—22no—
380C4×C61—41no—
381C4×C61—41no—
382Dic61—22no—
383Dic61—22no—
384Dic61—41no—
385Dic61—41no—
386Dic61—41no—
387Dic61—41no—
388Dic61#54611yescharacteristic
389Dic61#54611yescharacteristic
390Dic61#54711yescharacteristic
391Dic61#54711yescharacteristic
392C2×#529—611no—
393C2×#435—611no—
394C2×C8×D4—611no—
395#1985—611no—
396#1984—611no—
397#1870—611no—
398#1869—611no—
399#1869—611no—
400#1869—611no—
401#1818—611no—
402#1817—611no—
403#1798—611no—
404#1750—611no—
405#1729—611no—
406C2×#336—611no—
407C2×C61—42no—
408C2×C61—81no—
409C2×C61#233911yescharacteristic
410C2×C61C2×#40811yescharacteristic
411C2×C61#288011yescharacteristic
412C2×C61#296611yescharacteristic
413C2×C61#296811yescharacteristic
414C2×C61#299211yescharacteristic
415C2×C61#299411yescharacteristic
416D61—24no—
417C22×M16—611no—
418C23×C8—611no—
419C23×C8—611no—
420C23×C8—611no—
421#529—1224no—
422#529—1224no—
423C2×#126—611no—
424C2×#126—611no—
425C2×#125—611no—
426C2×#124#692311yescharacteristic
427C2×#123—611no—
428C2×#123—611no—
429C2×C22⋊Q8—611no—
430C2×#121—611no—
431C2×C4×Q8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×#117—611no—
436C2×#117—611no—
437C22×C42—611no—
438#435—1224no—
439C8×D4—1224no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×#97—611no—
451C2×C4×C8—611no—
452#336—611no—
453#336—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460#336—611no—
461#336—611no—
462#336—611no—
463#336—611no—
464C61#2247011yescharacteristic, complemented, Sylow
465C22×Q8C2×#692311yescharacteristic
466C22×D4—611no—
467C22×D4—611no—
468C22×D4C2×#692311yescharacteristic
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C2×M16—1222no—
475C2×M16—1222no—
476C2×M16—2441no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8—611no—
485C22×C8—1222no—
486C22×C8—1222no—
487C22×C8—1222no—
488C22×C8—1222no—
489C22×C8—1222no—
490C22×C8—1222no—
491C22×C8—2441no—
492C22×C8—2441no—
493C22×C8—2441no—
494#126—1224no—
495#126—1224no—
496#125—1224no—
497#124—24no—
498#123—1224no—
499#123—1224no—
500C22⋊Q8—1224no—
501#121—1224no—
502C4×Q8—1222no—
503C4×Q8—1222no—
504C4×D4—614no—
505C4×D4—614no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510#117—1222no—
511#117—1222no—
512#117—1222no—
513#117—1222no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4C2×#692311yescharacteristic
531C2×C22⋊C4C2×#692311yescharacteristic
532C2×C22⋊C4C2×#692311yescharacteristic
533C2×C22⋊C4C2×#692311yescharacteristic
534C2×C42—611no—
535C2×C42—611no—
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—1222no—
540C2×C42—1222no—
541C2×C42C2×#692311yescharacteristic
542C4⋊C8—1222no—
543C4⋊C8—1222no—
544C22⋊C8—1222no—
545C22⋊C8—1222no—
546C22⋊C8—1222no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—1222no—
550C22⋊C8—2441no—
551C22⋊C8—2441no—
552#97—1222no—
553C4×C8—1222no—
554C24—611no—
555C24C22×#692311yescharacteristic
556C24C22×#692311yescharacteristic
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—41no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—41no—
563C2×D4—614no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C22×C4—611no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—612no—
575C22×C4—612no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1222no—
599C22×C4—2441no—
600C22×C4C22×#692311yescharacteristic
601C22×C4C22×#692311yescharacteristic
602C22×C4C22×#692311yescharacteristic
603C22×C4C22×#692311yescharacteristic
604C22×C4C22×#692311yescharacteristic
605M16—2444no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—2444no—
631C2×C8—2444no—
632C2×C8—2444no—
633C4⋊C4—614no—
634C4⋊C4—1222no—
635C4⋊C4—1222no—
636C4⋊C4—1222no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1222no—
642C4⋊C4—1222no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—614no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4C22⋊#692314yes—
653C42—22no—
654C42—612no—
655C42—612no—
656C42—1221no—
657C42—1221no—
658C42—1221no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C42—1222no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—612no—
677C23—612no—
678C23—612no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23C2×C22⋊#692312yes—
684C23C23×#692311yescharacteristic
685Q8—44no—
686D4—44no—
687D4—1228no—
688D4—2444no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—611no—
702C2×C4—611no—
703C2×C4—611no—
704C2×C4—611no—
705C2×C4—611no—
706C2×C4—611no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—2444no—
734C2×C4—2444no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4C2×C22⋊#692312yes—
740C2×C4C2×C22⋊#692312yes—
741C2×C4#1451986412yes—
742C8—1222no—
743C8—1222no—
744C8—2441no—
745C8—2441no—
746C8—2441no—
747C8—2441no—
748C8—2441no—
749C8—2441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—614no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—1222no—
770C22—1222no—
771C22C22×C22⋊#692311yescharacteristic
772C22#41×#692311yescharacteristic
773C22#1684083111yescharacteristic
774C22C2×#1451986411yescharacteristic
775C22D61⋊#13111yescharacteristic
776C22D61⋊#13111yescharacteristic
777C22#1684084011yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—41no—
782C4—41no—
783C4—611no—
784C4—611no—
785C4—611no—
786C4—611no—
787C4—1222no—
788C4—1222no—
789C4—2441no—
790C4—2441no—
791C4—2441no—
792C4—2441no—
793C2—42no—
794C2—81no—
795C2—1224no—
796C2#2146232211yescharacteristic
797C2D61⋊#40811yescharacteristic
798C2#2146240711yescharacteristic
799C2#2146263311yescharacteristic
800C2#2146264511yescharacteristic
801C2#2146275611yescharacteristic
802C2#2146276911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×#124×C61C4
prime radicalC2×#14519748C4
cosocleC22×Dic61C24
hypercenterC2×#124#6923
hypocenterC61#22470
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840794C2semidirect
2. C2×#16840789C2semidirect
3. #21461993C2semidirect
4. #21461988C2semidirect
5. #21461796C2semidirect
6. #21461793C2semidirect
7. #21461793C2semidirect
8. #21461792C2semidirect
9. #21461712C2semidirect
10. #21461711C2semidirect
11. #21461677C2semidirect
12. #21461549C2semidirect
13. #21461485C2semidirect
14. #21461480C2semidirect
464. C61#22470semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168407942
C2×#168407892
#214619932
#214619882
#214617962
#214617932
#214617922
#214617122
#214617112
#214616772
#214615492
#214614852
#214614802
C2×#168402912
#2247061